Have a small weeping willow that was here when we bought the house. It had never been pruned so I did it. Now I have something invasive growing out of the tree with wide broad leaves! Also looks like sap or something is seeping from the tree.
Pruning during active growth will result in a tree bleeding sap.
Suckers should be pruned from the tree as soon as they appear.
Watch for signs of stress, pests and disease in the tree. Treat any pests with Neem Oil.
This link will refresh you on proper pruning.